7 Oct
2006
7 Oct
'06
9:37 p.m.
A curiosity: There seem to be 1.5 times as many primes of the form 2^N-3 as there are of the form 2^N+3. 2^N+3 is prime for N = 1 2 3 4 6 7 12 15 16 18 28 30 55 67 84 228 390 784 while 2^N-3 is prime for N = 3 4 5 6 9 10 12 14 20 22 24 29 94 116 122 150 174 213 221 233 266 336 452 545 689 694 850 (up to N=1000). The former sequence is divisible by 7 when N = 2 mod 3, while the latter is never a multiple of 7. Small primes other than 7 seem to strike both sequences equally. The large gaps (390-784, and 29-94) and general bunchiness (213, 221, 233; 689, 694) makes it hard to draw any firm conclusions. Rich